I. Solve using De Moivre's Theorem. Find the 2 square roots of 3 – 8i

Q: By writing the individual factors on the left in exponential form, performing the needed operations,…

A: Rectangular form to exponential form:  z=a+ib ------------------------------------------------------…

Q: Which quadratic equation has roots 2 + 6i and 2 – 6i? x2 – 4x + 13 = 0 O x2 + 4x + 13 = 0 Submit…

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Q: Find the cube roots of –64i and express them in trigonometric form.

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Q: Find the square root of the following complex number z = 1 + 7i

A: To find  the square root of z=1+7i i.e. 1+7i

Q: Solve the following complex roots and plot the solutions if (z – 5 + i)6 = -729.

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Q: In(In z1) O -0.5198 - 0.7636i O 1.4979 - 0.4636i O 1.5680 - 0.8205i 0.4498 - 0.3002i O O O

A: Let z=x+iy be a complex number. The polar form of the complex number is z=reiθ, where r=x2+y2 and…

Q: Solve the following  complex numbers in their rectangular form:…

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Q: -3X1 + 9X2 + X3 = 6

A: Given,        -3X1+9X2+X3=6       5X1-4X2+15X3=9            4X1-X2+2X3=15

Q: Find all Cubic Roots of Unity of -15+2i

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Q: Find the roots of the given complex number 1. z^3 = 2 – 3i

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Q: Find all complex square roots of 1+V3 i. In other words, find all complex solutions of x=1+/3 i.

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Q: Find the roots, including the complex ones, of 2x³– 3x? = 1 using Newton's method.

A: To find the roots using Newton's method, 2x3-3x2=12x3-3x2-1=0Let, f(x)=2x3-3x2-1…

Q: Find the cube roots of (a) 1+i (b) 2i-2 giving your answers in exponential form.

A: #(a) Find the cube roots of 1+i

Q: −j j sin² zdz

A: Consider I=∫-jjsin2zdz

Q: Solve the following complex roots and plot the solutions if (z – 5+ i)6 = -729.

A: Given z-5+i6=-729

Q: Solve by using the quadratic formula: x +10x+16=0 O A. 5+3i and 5-3i B. -5+3i and -5-3i O C. 3+5i…

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Q: Solve the equation using De Movier's theorem: x² – 2 – 2V3i = 0 %3D

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Q: Find the exact solution of the equation. 4sin-1x=pi

A: Now we will find the solution.  We know,  sin(pi/4) = 1/sqrt(2)

Q: Find the two square roots of 36i.       6i , - 6i

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Q: The complex cube roots of 1+ V3 i.

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Q: Find all complex square roots of -4i. In other words, find all complex solutions of x =-4i. i

A: Find the all complex solutions

Q: Find the fifth roots of the complex number 3 - 4i

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Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. -8 – 8i3 8+8i -16…

A: Explanation of the answer is as follows

Q: [(5+ 2i)(-1+ 4i) – 5260°]*

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Q: re cube roots of unity, tl w?) is

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Q: Solve the following complex numbers in their rectangular form. Use 4 decimal places for the…

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Q: (b). Apply Newton's Raphson method and find the roots of the equation e-2x = 5x + 2, correct to four…

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Q: Find all the complex fourth roots in rectangular form of w = 100 cos 57 - + i sin Zo (Type your…

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Q: Solve by finding the square roots. (Round to the nearest i y = x? – 121 X = or x =

A: y=x2-121

Q: Find the roots of the given complex number 1. z^5 = 4i

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Q: Find all solutions of the equation and express them in the form a + bi.

A: Consider the given equation x2+12x+1=0. Simplify the given equation. 2x2+x+22=02x2+x+2=0

Q: I. Solve using De Moivre's Theorem. Find the 9th roots of 12 – 13i

A: Consider the provided question, According to the given information, it is required to find 9th roots…

Q: Find three cube roots for the following complex number. 32√3 + 32i   w0= w1= w2=

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Q: b. Find the roots of √√√64 e¹.4i

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Q: Express the complex solutions of the equation z^n + 1 = 0, where n ∈ N, in  terms of roots of unity.

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Q: Solve by using the quadratic formula: x +10x+9 =0 A. 5+4i and 5– 4i B. -5 + 4i and –5– 4i C. 4+5i…

A: As we know that   If ax2+bx+c=0  then  x1,2=-b±b2-4ac2a.   Given;   x2+10x+9=0

Q: logz, Z3

A: This is a problem of complex analysis.

Q: Derive the quadratic formula for the zeros of ax2+ bx + c, where a, b, and c are complex numbers and…

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Q: Find all solutions of the equation and express them in the form a + bi.

A: Given: 70. t+3+3t=0

Q: . Find all complex solutions to the given equation (1) x3+8i =0

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Q: Find the cube root of -8i lying in the fourth quadrant of complex plan. إختر أحد الخيارات: 1- V3i 1+…

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Q: Find the roots of the equation z³ +2 – 2/3i = 0. %3| -

A: Given: z3+2-23i=0 So,  z3=-2+23iz3=2-1+3iz3=4-12+32i We know that z=rcosθ+isinθ=x+iy, where r=x2+y2,…

Q: Find the square roots of the given complex number by using result (10) and then confirm the result…

A: We can find the square root of complex number by using the formula.

Q: Find the two square roots of 36i.   3Ï2 + 3iÏ2, -3Ï2 - 3iÏ2

A: z=36i=0+36i Now, r=02+362=36 & θ=tan-1yx=tan-1360=tan-1∞=π2 Now the polar form is,…

Q: 2. Use the quadratic formula to find the roots of the equation: 5x - 4x +8 = 0. -4+ 12i 5. O x = 3…

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Q: Find the imaginary component if the nth root of a + bi is determined for a = 10, b = 8, and n = 7.…

A: Imaginary component of the function

Q: Find the complex roots of t

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Q: 4x + 0.5 x + 2.4 2x + 1.7

A: Solve for x

Q: Let n = Z and AABC be a right triangle with right angle at C. If sin A and sin B are the roots of…

A: What is Quadratic Equation: When a quadratic polynomial assumes the value zero, that equation is…